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Abstract: A certain complexity threshold is proposed which defines the term `complexnetwork- for RSN, e.g. Kauffman networks with s>=2 - more than two equallyprobable state variants. Such Kauffman networks are no longer Boolean networks.RSN are different than RWN and RNS. This article is the second one of threesteps in description of `structural tendencies- which are an effect of adaptiveevolution of complex RSN. This complexity threshold is based on the appearancesof chaotic features of a network during its random growth and disappearance ofsmall network effects. Distribution of damage size after small disturbancemeasured in a fraction of damaged nodes, or in number of damaged externaloutputs and degree of chaos is investigated using simulation. It is done duringgrowth up to N=4000 nodes for different: network types includingscale-free, numbers of node inputs K=2,3,4, fixed for a network and numbersof signal variants s=2,3,4,16. In this distribution two peaks emerge andin-between them there appears an area of zero frequency - this is the bestpractical criterion of complexity threshold found in the investigation. Nocritical points are found in the area of emerging complexity. A specialsimplified algorithm `reversed-annealed- is used which omits the problem ofcircular attractors. The investigated `transition- to chaos in respect to N isdifferent from the known phase transition near K=2 for s=2.



Author: Andrzej Gecow

Source: https://arxiv.org/







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